Panic Time?!?!

This is always sort of a frustrating time for me to be a baseball fan. Every year it seems people get hysterical when someone gets off to a slow start, when they just need to relax and let things develop. There are a lot of examples of people jumping to conclusions base on small samples. Your centerfielder is hitting .190? Bench him? After 37 AB’s, probably not. Your team is playing .500 ball after 10 games, so turn the whole roster over? No. The team has scored 51 runs in those 10 games, and has scored at least 4 runs in 9 of those 10 games, so make drastic changes to the lineup? I don’t think so! The solution is to have some patience and let everything settle, if you will.

Earlier I read Dexter Fowler was a “liability” in the lineup, because of his .189 batting average, so I’ll use him as an example. Dex’s batting average has come in 37 at bats, which is pretty obviously not very many. So how many is enough to actually worry? We can build a simple hypothesis test for a player’s batting average based on his current average, and his number of at bats. Given Dex’s ability to get on base (which is the real thing we care about, and deserves more analysis later), he needs to bat at least .250 to be a useful part of the lineup. If I’m Dan O’Dowd/Jim Tracy I’m going to want strong evidence that he’s not before I hit the panic button. Assuming at bats follow a typical binomial pattern, we test the hypothesis that the player is a .250 hitter after n at bats. It turns out that the number of AB’s that a player batting .189 can have before we feel truly confident that he’s not at least a .250 hitter is 111. (I’m more than willing to explain my math, if anyone asks.) That means Dexter only has 74 more AB's to get his average above .190. Don’t worry, something tells me he’ll do it.